# Full text of "Mathematical And Physical Papers - Iii"

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```ON  THE MOTION  OF  PENDULUMS.
105
to an infinite cylinder moving with the same linear velocity, we have by the formulae of Art. 31
dF = Jc'M'n -j^ , where M' = 7rpa?dr, -TJ.==T-JI-
If G be the moment of the resistance, I the whole length of the cylinder, we have, putting n = TTT~I,
12r     dt ' whence
i        /-i           \-i       *7T iC OCt/ I                              /ir»r\
loge(l -m)   = -~24J~ ...............GOD),
/ being the moment of inertia.
Expressing / in terms of the same quantities as in the case of the disk, we get from (147) and (165)
loglo (1 - m)-> = logw
...... (166),
and ffp is the weight of a cubic millimetre of water, or the 1000th part of a gramme. The numerical values of JUL ', T, R, W have been already given, but // must be reduced from square inches to square millimetres. The cylinders, of which three were tried in succession, had all the same length, namely, 249 millimetres. Their circumferences, calculated from their weights and expressed in millimetres, were 21*1, 11*2, and 0*87, and the time of four oscillations was 92s, 91s, 91s. The values of m calculated from these data by means of the formula (147) are 0*4332, 0*2312, and 0*01796. For the first and second of these values, m%' may be obtained by interpolation from the table given in Part I. ; for the third it will be sufficient to employ the second of the formula} (115).
The following are the results :
Cylinder, No. 1.          No. 2.                   No. 3.
m, by experiment .........    0*0400           0*0260            0*0136
m, by theory ...............    0*0413            0'0291            0*0113
Difference    - 0'0013        - 0*0031
+ 0*0023
The differences between the results of theory arid experiment are perhaps as small as could reasonably be expected, when it is
II```